1. Field of the Invention
The present invention relates to a cylindrical shape measuring apparatus for measuring the surface state (surface shape) of, for example, a cylindrical lens or cylindrical mirror by utilizing interference, as well as a method of measuring the system errors of such an apparatus. More specifically, the present invention pertains to a cylindrical shape measuring apparatus which is capable of measuring the surface shape accurately and two-dimensionally by removing the system errors inherent in the apparatus.
2. Description of the Related Art
There has been a demand for an apparatus capable of measuring the optical surface of an optical member, such as a cylindrical lens or a cylindrical mirror, with a high degree of accuracy, e.g., on the order of one-tenth of a wavelength or less. Various interference measuring apparatuses (light wave interferometers) of the type which utilize the interference principle, are extensively used as such an apparatus for measuring the optical surface. Particularly, various types of interference measuring apparatuses capable of accurate and quantitative measurement have been put into practical use in recent years owing to the wide use of lasers exhibiting excellent coherence and the development of electronics.
However, in the measuring operation by the interference measuring apparatus, since a difference of two surface shapes is read, if one of the surfaces is not an ideal one, the measuring operation must be conducted a few times under different measuring conditions so as to obtain surface shape errors in each of the operations by analyzing the results of the measurement.
In such a light wave interferometer, absolute accuracy is guaranteed by measuring error components inherent in the interferometer, which are generated by manufacturing errors of the optical parts constituting the interferometer, called system errors, and then by subtracting the measured inherent error components from the shape measuring data of an object to be measured, such as a lens or a mirror. Such an absolute accuracy guaranteeing method, which is used for a Twyman-Green interferometer, has been disclosed by J. H. Bruning in APPLIED OPTICS Vol. 13, No. 11 (1974) 2693. The absolute accuracy guaranteeing method for a Fizeau interferometer has been disclosed by B. E. Truax in SPIE Vol. 966 (1988) 130.
FIG. 1 schematically shows a typical Twyman-Green interferometer.
In FIG. 1, reference numeral 101 denotes a He-Ne laser, which serves as a light source, reference numeral 102 denotes a beam expander for expanding the aperture of an incident beam, and reference numeral 103 denotes a polarization beam splitter which constitutes the interferometer. Reference numerals 104a and 104b denote quarter-wave plates for rotating the angle of polarization by 90 degrees between the rays of light that are incident thereon for the first time and the rays of light that are incident thereon for the second time. Reference numeral 105 denotes a reference mirror, reference numeral 110 denotes a condenser lens for generating a reference spherical surface, and reference numeral 106 denotes an object to be measured. Reference numeral 107 denotes a polarizing plate, reference numeral 108 denotes a CCD camera for observing an interference fringes, and reference numeral 109 denotes a computer for operating interference fringe image.
In the thus-arranged structure, the coherent rays of light emerging from the light source 101 are expanded by the beam expander 102 in terms of the aperture, and then are incident on the polarization beam splitter 103 which divides the incident rays of light into a light La, which propagates toward the reference mirror 105, and a light Lb, which is directed toward the object to be measured 106.
The light La, which is directed toward the reference mirror 105, emerges from the quarter-wave plate 104a circularly polarized. The circularly-polarized light that is reflected by the reference mirror 105 passes through the quarter-wave plate 104a again. The quarter-wave plate 104a rotates the angle of polarization by 90 degrees between the light that has passed therethrough for the first time and the light that has passed therethrough for the second time. The introduced plane-polarized light passes through the polarization beam splitter 103 and propagates toward the CCD camera 108.
The light Lb, which is directed toward the object to be measured 106, emerges from the quarter-wave plate 104b circularly polarized. The circularly-polarized light is converted into a spherical wave by the condenser lens 110, and is then reflected by the object to be measured 106 having a spherical shape. The reflected light passes through the condenser lens 110 and then the quarter-wave plate 104b again. The quarter-wave plate 104b rotates the angle of polarization by 90 degrees between the light that is incident thereon for the first time and the light that is incident thereon for the second time. The plane-polarized light emerging from the quarter-wave plate 104b is reflected by the polarization beam splitter 103, whereby it is directed toward the CCD camera 108. At that time, the two plane-polarized lights La and Lb, which are perpendicular to each other, are caused to interfere by the action of the polarizing plate 107. The resultant interference fringes are observed on the CCD camera 108.
The observed interference fringes are considered to be the display of contours whose intervals are one half the wavelength and which represent a difference between the wavefront shape of the wave light, which has been divided by the polarization beam splitter 103 and then reflected by the reference mirror 105, and the wavefront shape of the wave light, which has been divided by the polarization beam splitter 103 and then reflected by the object to be measured 106.
Thus, if the reference mirror 105 has an ideal flat surface and if the condenser lens 110 is completely aplanatic, the obtained interference fringes represent the spherical surface errors of the object to be measured 106.
However, it is impossible in a practical way to manufacture an ideal flat surface or an aplanatic lens. Thus, the observed interference fringes contain the flat surface errors of the reference lens 105 and the aberration of the condenser lens 110.
Hence, the previously mentioned article by Bruning has proposed a method of removing the error components inherent in the interferometer, such as the flat surface errors of the reference mirror 105 or the aberration of the condenser lens 110.
In this method, three measurement operations are performed each having measuring systems 1, 2 and 3 shown in FIGS. 2(A), 2(B) and 2(C).
Each of the measurement results W.sub.1 (x, y), W.sub.2 (x, y) and W.sub.3 (x, y) obtained by the corresponding measuring systems 1, 2 and 3 is considered to be the difference between the wavefront errors in the measuring optical path and those in the reference optical path, and is given by: EQU W.sub.1 (x, y)=W.sub.M (x, y)-W.sub.R (x, y) (1) EQU W.sub.2 (x, y)=W.sub.M '(x, y)-W.sub.R (x, y) (2) EQU W.sub.3 (x, y)=W.sub.C (x, y)-W.sub.R (x, y) (3)
where W.sub.R is the wavefront of the reference light, W.sub.M is the wavefront of the measured light reflected at the surface measuring position in FIG. 2(A), W.sub.M ' is the wavefront of the measured light reflected by the object to be measured 106 which has been rotated around the optical axis by 180 degrees, as shown in FIG. 2(B), and W.sub.C is the wavefront of the measured light cat's eye reflected, as shown in FIG. 2 (C). Under the assumption that the wavefront aberration does not change as the wave light propagates, W.sub.R, W.sub.M, W.sub.M ' and W.sub.C are given by EQU W.sub.R (x, y)=W.sub.i (x, y)+W.sub.r (x, y) (4) EQU W.sub.M (x, y)=W.sub.i (x, y)+W.sub.L (x, y)+W.sub.S (x, y)(5) EQU W.sub.M '(x, y)=W.sub.i (x, y)+W.sub.L (x, y)+W.sub.S (-x, -y)(6) EQU W.sub.C (x, y)=W.sub.i (-x, -y)+{W.sub.L (x, y)+W.sub.L (-x, -y)}/2(7)
where W.sub.i (x, y) represents the wavefront errors of the light source, W.sub.r (x, y) represents the wave front errors (x2) of the reference mirror 105, W.sub.L (x, y) represents the wavefront errors (x2) of the condenser lens 120, and W.sub.S represents the wave front error (x2) of the object to be measured 106.
From equations (1) through (7), we have an equation (8) which expresses the system errors as follows: EQU W.sub.L (x, y)-W.sub.r (x, y)={W.sub.1 (x, y)-W.sub.2 (-x, -y) +W.sub.3 (x, y)+W.sub.3 (-x, -y)}/2 (8)
where W.sub.2 (-x, -y) indicates that the address of the measurement data W.sub.2 obtained in the second measuring operation is rotated about the optical axis by 180 degrees.
When the surface shape other than the spherical surface, e.g., the rotation asymmetric surface shape of the object to be measured, such as a cylindrical lens or a cylindrical mirror, is to be measured by the interferometer shown in FIG. 1, a cylindrical wavefront must be generated using a cylindrical lens in the condenser lens.
In that case, the light reflected by the object to be measured in the system indicated by FIG. 2 (C) returns to the condenser lens as the light wavefront which is symmetric with respect to the focusing line.
Therefore, the equation (7) is transformed to EQU W.sub.C (x, y)=W.sub.i (x, y)+{W.sub.L (x, y)+W.sub.L (x, -y)}/2 (9)
Consequently, the system errors cannot be expressed by the equation (8).